Jeremy Corbyn is leading a cross-party effort to force ministers to publish details of the impact of their policies broken down by gender, race, age, disability, class and region, after analysis showed women continue to bear the brunt of austerity.

The Labour leader has signed a letter with 126 other MPs, including members of his own party, the Liberal Democrats, SNP and Greens, calling for an immediate equality assessment of all government policies.

The letter to the education secretary, Justine Greening, whose brief covers equalities, accuses the government of failing in its duty to sufficiently consider the impact of its actions on all groups in society.

A financial model developed by Yvette Cooper, the senior Labour backbencher, and House of Commons library statisticians found that 86% of savings to the Treasury from tax and benefit changes since 2010 had come from women.

Labour said the latest budget did nothing to change that, meaning women had been hit six times harder by austerity measures than men since the Conservatives came to power in 2010.

The letter, co-signed by Corbyn, Dawn Butler, the shadow equalities secretary, Jo Swinson, the deputy Lib Dem leader, Angela Crawley, the SNP spokeswoman on equalities, and Caroline Lucas, the co-leader of the Greens, said: “If the government continues in this manner there can be no public confidence that the public sector equality duty is being fulfilled.

“We are calling on the government to undertake and publish a comprehensive cumulative equality impact assessment of all government policies. This assessment must include analysis of the impact of all its policies in relation to gender, race, age, disability, class and region.

“We urge the adoption of this proposal as a matter of urgency so the government can assess the overall impact of its policies on the population as a whole and specific groups sharing protected characteristics.”

Labour is committed to auditing every budget for gender impact and promoting gender equality at the heart of economic policymaking.

Butler said the budget had not once mentioned women and was “more of the same from the chancellor, with women and our diverse communities again being forced to bear the brunt of this failed Tory economic project”.

She said: “Despite Theresa May herself warning in 2010 that cuts would disproportionately impact on those with protected characteristics, her government continues to pursue an economic agenda based on discrimination and inequality which has hit women the hardest.”

A spokesman for the government said the Treasury considered the equality impacts of individual policies on those with protected characteristics – including gender, race and disability – in line with its legal obligations and what it said was its strong commitment to equality.

“We are fully committed to equality and carefully consider how those with protected characteristics are impacted by government policy,” he said. “About 1.4 million more women are in work since 2010, and the full-time gender pay gap is at a record low. We publish comprehensive distributional analysis at every budget, which shows that the state continues to be highly redistributive.”

The Treasury said analysis published by others tended to exclude spending on public services that directly benefited households, such as the NHS, and could assume that all households fully take up all benefits to which they are entitled and exclude tax measures for which there was not sufficient data to attribute the impact to individual households.

It said analysis published by other organisations trying to show the impact of policies by gender made strong assumptions about how income was shared within households.